Terahertz wave optical element and method for producing terahertz wave optical element
A terahertz wave lens includes a substrate having a surface provided with an uneven structure that changes a phase of the terahertz wave. The uneven structure includes a plurality of holes that are periodically arranged. The uneven structure includes a plurality of regions where the plurality of holes are arranged. A height of the hole in a thickness direction of the substrate and a width of the pillar differ for each of the regions. Outer end portions of the uneven structure in the thickness direction are located on the same plane.
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The present disclosure relates to a terahertz wave optical element and a method for producing a terahertz wave optical element.
BACKGROUNDIn recent years, a technique that uses an electromagnetic wave (terahertz wave) in a terahertz band to enable safe and highly accurate analysis has attracted attention. In order to use the terahertz wave, a condensing optical system (lens or the like) that collimates or concentrates the terahertz wave is required. In order to avoid an increase in size of the condensing optical system, it is preferable that a lens as small as possible is used. In the related art, as a lens that is smaller than a spherical lens generally used and can realize a relatively high NA, there has been known a flat lens (metal lens) which has a flat plate shape and in which a fine uneven structure (dielectric uneven structure arrangement) is formed on the surface of a substrate.
For example, Patent Literature 1 (Japanese Patent No. 6356557) discloses a technique by which an SOI substrate in which an etching stopper layer made of SiO2 and a silicon layer made of Si are sequentially formed on a Si substrate is prepared, a mask corresponding to the pattern of an uneven structure is formed on the surface of the silicon layer of the SOI substrate, and portions of the silicon layer which are not covered with the mask are removed by etching; and thereby, the above-described uneven structure is formed. In addition, Patent Literature 2 (Japanese Unexamined Patent Publication No. 2007-57622) discloses a technique by which a method that is a combination of laser interference and laser processing is used to form an uneven structure, in which the height of the structure is spatially modulated, on a substrate.
SUMMARYAccording to the technique described in Patent Literature 1, since etching is stopped in a stage where the etching stopper layer is exposed, the height of the uneven structure (namely, the etching depth) can be made uniform. However, since SiO2 used as the etching stopper layer has a property of absorbing light in a terahertz region, SiO2 is not suitable for a terahertz wave optical element. In addition, in the technique described in Patent Literature 2, high brightness processing laser, an interference mask, and the like are required and a process for forming the uneven structure becomes complicated, which is a problem. In addition, since the height of the uneven structure (position of the outermost surface) is irregular, an aberration is likely to occur, which is a problem.
An object of one aspect of the present disclosure is to provide a terahertz wave optical element and a production method of the same which can suppress the occurrence of an aberration while reducing the size.
According to one aspect of the present disclosure, there is provided a terahertz wave optical element including: a substrate having a surface provided with an uneven structure that changes a phase of the terahertz wave. The uneven structure includes a plurality of unevenness forming portions formed of recessed portions that are periodically arranged. The uneven structure includes a plurality of regions where the plurality of unevenness forming portions are arranged. A height of the unevenness forming portion in a thickness direction of the substrate and a width of the unevenness forming portion in a direction orthogonal to the thickness direction differ for each of the regions. Outer end portions of the uneven structure in the thickness direction are located on the same plane.
In the terahertz wave optical element, the height and the width of the unevenness forming portion forming the uneven structure differ for each of the regions. Accordingly, a phase difference that differs for each of the regions can be generated for the terahertz wave transmitted through the substrate. In addition, since the substrate on the surface of which the uneven structure is formed is used to be able to further reduce the thickness of the lens than that of a spherical lens or the like, the size of the lens can be reduced. Furthermore, since the height positions of the outer end portions of the uneven structure in the thickness direction are aligned, the occurrence of an aberration can be suppressed.
A distance between centers of the unevenness forming portions adjacent to each other may be constant. According to the configuration, since the arrangement interval (period) between the unevenness forming portions is constant, the design of the arrangement of the unevenness forming portions is facilitated.
The larger the width of the unevenness forming portion is, the higher the height of the unevenness forming portion may be. According to the configuration, since the microloading effect in etching is used, the uneven structure where the height and the width of the unevenness forming portion differ for each of the regions can be easily formed.
The plurality of regions may be formed of N (N is an integer of 2 or more) regions including a first region to an Nth region that are arranged along a predetermined direction. An effective refractive index of each of the plurality of regions may be further decreased in a stepwise manner as the region is shifted from the first region toward the Nth region. According to the configuration, since the plurality of regions are arranged such that the effective refractive index is further decreased in a stepwise manner as the region is shifted from the first region toward the Nth region, the terahertz wave optical element can serve as a refractive index distribution type lens.
The height of the unevenness forming portion belonging to each of the regions may be further increased as the region is shifted from the first region toward the Nth region. According to the configuration, the phase difference between the regions can be more efficiently generated than when only the width of the unevenness forming portion differs for each of the regions.
The plurality of regions may include a first phase difference region where a phase difference between the regions adjacent to each other is set to a first phase difference, and a second phase difference region where a phase difference between the regions adjacent to each other is set to a second phase difference smaller than the first phase difference. According to the configuration, phase distribution design can be more flexibly performed than when the phase differences between the regions are equal.
At least one of the regions, in which the width of the unevenness forming portion in the uneven structure is a threshold value determined in advance or less, may be the second phase difference region. In addition, at least the first region may form the second phase difference region. According to the configuration, for example, when the uneven structure is formed by etching, in a portion in which the microloading effect is relatively remarkable and it is difficult to accurately produce the unevenness forming portion having the width and the height corresponding to a phase distribution designed in advance, the step size of the phase difference between the regions is made small, so that a deviation (production error) of the phase distribution from the design value can be compensated.
The unevenness forming portion may include a plurality of repetition units each including one set of the plurality of regions. The plurality of repetition units may be arranged along the predetermined direction. At least one of the plurality of repetition units may be formed to have a phase distribution having a width larger than 2π. In order to appropriately obtain the lens effect, it is preferable that the repetition unit has a phase distribution having a width of 2π or more. Meanwhile, due to the above-described production error caused by the microloading effect, the width of the phase distribution of the repetition unit may be smaller than 2π. According to the configuration, it is possible to reduce a possibility that the width of the actual phase distribution is smaller than 2π in the repetition unit formed to have a phase distribution having a width larger than 2π.
The height and the width of the unevenness forming portion corresponding to each of the plurality of regions may be sized so as to suppress reflection of the terahertz wave at an interface between the uneven structure and air. According to the configuration, since a reflection prevention layer is not required to be provided separately from the unevenness forming portion, the reflection of the terahertz wave at the interface between the uneven structure and air can be suppressed while an increase in size of the terahertz wave optical element is prevented.
According to one aspect of the present disclosure, there is provided a method for producing a terahertz wave optical element, the method including: a first step of determining a pattern of an uneven structure that changes a phase of the terahertz wave; a second step of forming an etching mask, which corresponds to the pattern, on a surface of a substrate that is flat; a third step of performing anisotropic etching on the substrate in a state where the etching mask is formed on the surface of the substrate, to form the uneven structure in the surface of the substrate, the uneven structure including a plurality of unevenness forming portions formed of recessed portions that are periodically arranged; and a fourth step of removing the etching mask from the surface of the substrate. The uneven structure includes a plurality of regions where the plurality of unevenness forming portions are arranged. A height of the unevenness forming portion in a thickness direction of the substrate and a width of the unevenness forming portion in a direction orthogonal to the thickness direction differ for each of the regions.
According to the production method, the terahertz wave optical element exhibiting the above-described effects can be produced. In addition, since the surface of the substrate is etched with the etching mask, the height positions of portions covered with the etching mask (namely, portions that are not removed by etching) can be aligned to a constant position. In addition, since the microloading effect in etching is used, a structure where both of the height and the width of the unevenness forming portion differ for each of the regions can be easily produced.
In the first step, the pattern of the uneven structure may be determined such that a distance between centers of the unevenness forming portions adjacent to each other is constant. According to the configuration, the design of the arrangement of the unevenness forming portions is facilitated.
In the first step, the pattern of the uneven structure may be determined such that the plurality of regions are formed of N (N is an integer of 2 or more) regions including a first region to an Nth region that are arranged along a predetermined direction, and an amount of etching per unit area of each of the plurality of regions is further increased in a stepwise manner as the region is shifted from the first region toward the Nth region. According to the configuration, the plurality of regions where the effective refractive index is further decreased in a stepwise manner as the region is shifted from the first region toward the Nth region can be formed, and the terahertz wave optical element serving as a refractive index distribution type lens can be obtained.
The first step may include a step of acquiring information indicating a relationship between the width of the unevenness forming portion and an etching depth, and a step of determining the width of the unevenness forming portion, which is arranged in each of the regions, based on the information indicating the relationship and a design value of a phase distribution determined in advance. According to the configuration, since the width of the unevenness forming portion of each of the regions is determined in consideration of the relationship between the width of the unevenness forming portion and the etching depth (namely, the magnitude of the influence of the microloading effect), the occurrence of a production error (deviation from the design value) caused by the microloading effect can be suppressed.
In the first step, the width of the unevenness forming portion arranged in each of the regions may be determined such that the plurality of regions include a first phase difference region and a second phase difference region. The first phase difference region is a region where a phase difference between the regions adjacent to each other is set to a first phase difference. The second phase difference region is a region where a phase difference between the regions adjacent to each other is set to a second phase difference smaller than the first phase difference. According to the configuration, phase distribution design can be more flexibly performed than when the phase differences between the regions are equal.
In the first step, the width of the unevenness forming portion arranged in each of the regions may be determined such that at least one of the regions, in which the width of the unevenness forming portion in the uneven structure is a threshold value determined in advance or less, is the second phase difference region. In addition, in the first step, the width of the unevenness forming portion arranged in each of the regions may be determined such that at least the first region forms the second phase difference region. According to the configuration, in a portion in which the microloading effect is relatively remarkable and it is difficult to accurately produce the unevenness forming portion having the width and the height corresponding to a phase distribution designed in advance, the step size of the phase difference between the regions is made small, so that a deviation (production error) of the phase distribution from the design value can be compensated.
In the first step, the width of the unevenness forming portion arranged in each of the regions may be determined such that the unevenness forming portion includes a plurality of repetition units each including one set of the plurality of regions, the plurality of repetition units are arranged along the predetermined direction, and at least one of the plurality of repetition units has a phase distribution having a width larger than 2π. According to the configuration, it is possible to obtain the terahertz wave optical element which reduces a possibility that the width of the actual phase distribution is smaller than 2π in the repetition unit formed to have a phase distribution having a width larger than 2π.
In the first step, the width of the unevenness forming portion arranged in each of the regions may be determined such that the height and the width of the unevenness forming portion corresponding to each of the plurality of regions are sized so as to suppress reflection of the terahertz wave at an interface between the uneven structure and air. According to the configuration, since a reflection prevention layer is not required to be provided separately from the unevenness forming portion, it is possible to obtain the terahertz wave optical element that can suppress the reflection of the terahertz wave at the interface between the uneven structure and air while preventing an increase in size of the terahertz wave optical element.
According to one aspect of the present disclosure, it is possible to provide a terahertz wave optical element and a production method of the same which can suppress the occurrence of an aberration while reducing the size.
Hereinafter, an embodiment of the present disclosure will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same reference signs will be used for the same or equivalent components, and duplicated descriptions will be omitted.
[Terahertz Wave Lens]
As illustrated in
The terahertz wave lens 1 includes a substrate 2 having a disk shape. The substrate 2 is made of a material (for example, silicon or the like) that is transparent in a terahertz region. In the present embodiment, the substrate 2 is made of high-resistance silicon. In the present embodiment, as one example, the diameter of the substrate 2 is 45 mm. The thickness of the substrate 2 is, for example, approximately 0.5 mm to 1 mm. A fine uneven structure 3 is formed in one main surface (surface) of the substrate 2, the one main surface intersecting a thickness direction D of the substrate 2. The uneven structure 3 serves as a phase modulation layer that changes the phase of a terahertz wave which is transmitted through the uneven structure 3.
The uneven structure 3 includes a plurality of pillars 31 (unevenness forming portions) that are periodically arranged. As illustrated in
Upper surfaces of the plurality of pillars 31 form outer end portions 3a of the uneven structure 3 in the thickness direction D. The outer end portions 3a (namely, the upper surfaces of the plurality of pillars 31) of the uneven structure 3 are located on the same plane. The uneven structure 3 includes the bottom portions 3b, which are located inward from the outer end portions 3a, in portions (namely, portions in which the pillars 31 are not formed) between the plurality of pillars 31. The length in the thickness direction D between the upper surface (outer end portion 3a) of the pillar 31 and the bottom portion 3b that surrounds the pillar 31 when viewed in the thickness direction D is defined as a height h (refer to
As illustrated in
Each of the repetition units RU includes a plurality of regions (a first region to an Nth region) that are arranged in the radial direction from a center P side toward an outer edge side of the substrate 2. Here, N is the number of regions included in one repetition unit RU, and is an integer of 2 or more. In the present embodiment, as one example, N is 9. Namely, each of the repetition units RU includes nine regions A1 to A9. As illustrated in
In the plurality of pillars 31 arranged in the same region, the heights h in the thickness direction D coincide with each other and the widths (in the present embodiment, diameters d (refer to
As illustrated in
In addition, the height h of the pillar 31 belonging to each of the regions A1 to A9 is further increased as the region is shifted from the region A1 toward the region A9. As described above, the height positions (positions in the thickness direction D) of the upper surfaces (outer end portions 3a) of the plurality of pillars 31 are aligned. Therefore, the height positions of the bottom portions 3b of the regions A1 to A9 are further moved toward the inside of the substrate 2 as the region is shifted from the region A1 toward the region A9. As described above, since the diameter d of the pillar 31 differs for each region, the effective refractive indexes of the regions A1 to A9 differ from each other, and the thickness of the uneven structure 3 (namely, the height h of the pillar 31) differs for each region, so that the phase difference between the regions can be further increased.
The height h of the pillar 31 is set to, for example, approximately one wavelength (125 μm) of the terahertz wave to be operated. However, the height h of the pillar 31 differs for each of the regions A1 to A9 due to a microloading effect occurring during etching to be described later. In the present embodiment, as one example, in each of the repetition units RU, the maximum value of the heights h of the pillars 31 (namely, the height h of the pillar 31 belonging to the region A9) is approximately 120 μm, and the minimum value of the heights h of the pillars 31 (namely, the height h of the pillar 31 belonging to the region A1) is approximately 95 μm. In addition, the maximum value of the diameters d of the pillars 31 (namely, the diameter d of the pillar 31 belonging to the region A1) is approximately 25 μm, and the minimum value of the diameters d of the pillars 31 (namely, the diameter d of the pillar 31 belonging to the region A9) is approximately 13 μm.
As illustrated in
Subsequently, anisotropic etching (anisotropic dry etching) is performed using the photoresist R remaining on the substrate 2 as an etching mask (S5). Accordingly, portions (silicon regions) of the substrate 2, the portions not being covered with the photoresist R, are removed.
Subsequently, the photoresist R remaining on the substrate 2 is removed (S6). With the above process, the terahertz wave lens 1 in which the uneven structure 3 described above is formed in the surface of the substrate 2 is obtained.
A design (design of the diameter d of the pillar 31 belonging to each of the regions A1 to A9) that takes into consideration the above-described microloading effect will be described in more detail with reference to
When etching (experiment) is performed in advance on the same processing target (substrate 2) using the same etching condition as that of etching to be performed in the production step (S5), a relationship between the diameter d of the pillar 31 (namely, the gap between the pillars 31) and the microloading effect as shown in
The broken line of
Meanwhile, the solid line of
For example, when the material (namely, a region to be removed by etching) of the uneven structure and the material of the substrate which is a foundation differ from each other, the etching is stopped on the surface of the substrate, so that the height of each of the pillars forming the uneven structure is constant. In such a case, the microloading effect is not required to be considered. However, as in the present embodiment, when the uneven structure is formed in the surface of the substrate itself, and regions where the microloading effect is remarkable (in the example of
Therefore, in the present embodiment, information indicating the relationship between the radius (or the diameter d) of the pillar 31 and the height h of the pillar 31 obtained by etching, as shown in
In the normal phase distribution design indicated by the broken line in
In the phase distribution design of the present embodiment indicated by the solid line in
The region where the microloading effect is remarkable is, for example, a region where the diameter d of the pillar 31 is a threshold value Δd determined in advance or more (namely, a region where the gap between the pillars 31 is a certain value or less). For example, in the example of
As described above, the phase is equally divided in the normal phase distribution design, whereas in the phase distribution design of the present embodiment, the number of divisions of the phase is further increased in the regions where the microloading effect is remarkable than in the regions where the microloading effect is not remarkable. In a portion in which the microloading effect is relatively remarkable and it is difficult to accurately produce the pillar 31 having the diameter d and the height h corresponding to the phase distribution designed in advance, the step size of the phase difference between regions is made small, so that a deviation (production error) of the phase distribution from the design value can be compensated.
Incidentally, as described above, the width (length in the radial direction) of the plurality of repetition units RU is further decreased gradually as the repetition unit RU is away from the center P. Namely, the width of each of the plurality of regions included in the repetition unit RU is further decreased gradually as the region is away from the center P. For this reason, for example, there is a case where in the repetition unit RU which is located in the vicinity of the outer edge of the substrate 2 and has a very small width, it is difficult to increase the number of deviations of the phase even in a region where the diameter d of the pillar 31 is the threshold value Δd or more. In such a repetition unit RU, the number of divisions of the phase in a region where the diameter d of the pillar 31 is a predetermined value or more is not necessarily required to be increased. For example, the repetition unit RU in the vicinity of the outer edge of the substrate 2 may have eight regions having a phase difference every π/4 designed according to the normal phase distribution design.
In addition, in the phase distribution design of the present embodiment, the repetition unit RU is formed to have a phase distribution having a width larger than 2π. Specifically, in the normal phase distribution design, the phase difference of regions having the maximum phase difference (regions corresponding to the regions A1 and A2 in the phase distribution design of the present embodiment) coincides with 2π such that the ideal phase distribution (namely, the phase distribution having a width of 2π) which is wrapped every 2π is approximated. On the other hand, in the phase distribution design of the present embodiment, the height h and the diameter d of the pillar 31 belonging to the region A1 are adjusted that the phase difference of the region A1 having the maximum phase difference is larger than 2π. In order to appropriately obtain the lens effect, it is preferable that the repetition unit RU has a phase distribution having a width of 2π or more. Meanwhile, due to the above-described production error caused by the microloading effect, the width of the phase distribution of the repetition unit RU may be smaller than 2π. Therefore, in the present embodiment, the repetition unit RU is formed to have a phase distribution having a width larger than 2π. Accordingly, a possibility that the width of the actual phase distribution of the repetition unit RU is smaller than 2π can be reduced.
In the present embodiment, as one example, the phase difference of the region A2 is set to π/8 with respect to the region A3, and the phase difference of the region A1 is set to a magnitude between π/8 and π/4 with respect to the region A2. Accordingly, the repetition unit RU has a phase distribution having a width larger than 2π in the entirety of the regions A1 to A9.
Gn=p−dn (2)
Gn+1=p−dn+1 (3)
Gm=p−(dn/2+dn+1/2) (4)
Here, the diameter dn is larger than the diameter dn+1. As a result, a size relationship between the gaps Gn, Gn+1, and Gm is “Gn<Gm<Gn+1”. Namely, since the period p of the plurality of pillars 31 is constant over the entirety of the uneven structure 3, the gap Gm having an intermediate size between the size of the gap Gn in the region An and the size of the gap Gn+1 in the region An+1 is formed between the region An and the region An+1. Accordingly, the magnitude of the microloading effect occurring in the vicinity of the boundary between the region An and the region An+1 is a magnitude between the magnitude of the microloading effect occurring in the region An and the magnitude of the microloading effect occurring in the region An+1. As a result, the pillar 31 having a height between the height of the pillar 31 corresponding to the region An and the height of the pillar 31 corresponding to the region An+1 is formed in the vicinity of the boundary between the region An and the region An+1 adjacent to each other. In other words, the bottom portion 3b having a height position between the height position of the bottom portion 3b in the region An and the height position of the bottom portion 3b in the region An+1 is formed in the vicinity of the boundary between the region An and the region An+1.
[Modification Example of Uneven Structure]
Next, a modification example (uneven structure 3A) of the uneven structure will be described with reference to
In the present embodiment, as one example, the hole 32 is formed of a recessed portion (bottomed hole) that has a columnar shape and is provided in the surface of the substrate 2. As illustrated in
In the uneven structure 3A, portions of the surface of the substrate 2, the portions not being provided with the holes 32, form the outer end portions 3a of the uneven structure 3A in the thickness direction D. The outer end portions 3a of the uneven structure 3A are located on the same plane. Specifically, the outer end portions 3a of the uneven structure 3A are continuously formed along the same plane. In the uneven structure 3A, a bottom portion of each of the holes 32 forms the bottom portion 3b of the uneven structure 3A. The length in the thickness direction D between the outer end portion 3a and the bottom portion (bottom portion 3b) of the hole 32 is defined as the height h (refer to
In the plurality of holes 32 arranged in the same region, the heights h in the thickness direction D coincide with each other and the widths (in the present embodiment, the diameters d (refer to
As illustrated in
In addition, the height h of the hole 32 belonging to each of the regions A1 to A9 is further increased as the region is shifted from the region A1 toward the region A9. Namely, the height positions of the bottom portions 3b of the regions A1 to A9 are further moved toward the inside of the substrate 2 as the region is shifted from the region A1 toward the region A9. As described above, since the diameter d of the hole 32 differs for each region, the effective refractive indexes of the regions A1 to A9 differ from each other, and the thickness of the uneven structure 3A (namely, the height h of the hole 32) differs for each region, so that the phase difference between the regions can be further increased.
The height h of the hole 32 is set to, for example, approximately one wavelength (125 μm) of the terahertz wave to be operated. However, the height h of the hole 32 differs for each of the regions A1 to A9 due to a microloading effect occurring during etching to be described later. In the present embodiment, as one example, in each of the repetition units RU, the maximum value of the heights h of the holes 32 (namely, the height h of the hole 32 belonging to the region A9) is approximately 125 μm, and the minimum value of the heights h of the holes 32 (namely, the height h of the hole 32 belonging to the region A1) is approximately 95 μm. In addition, the maximum value of the diameters d of the holes 32 (namely, the diameter d of the hole 32 belonging to the region A9) is approximately 25 μm, and the minimum value of the diameters d of the holes 32 (namely, the diameter d of the hole 32 belonging to the region A1) is approximately 11 μm.
Similar to the uneven structure 3, the uneven structure 3A can be produced by using, for example, the above-described photolithography technology. Namely, similar to the uneven structure 3, the uneven structure 3A can be produced by the procedure illustrated in
Even when the uneven structure 3A is used, similar to when the uneven structure 3 is used, the design (design of the diameter d of the hole 32 belonging to each of the regions A1 to A9) that takes into consideration the microloading effect can be performed. Specifically, instead of the information indicating the relationship between the radius of the pillar 31 and the etching depth (height of the pillar 31 obtained by etching) shown in
Meanwhile, it is preferable that the phase difference is sharply changed in a step shape at the boundary between the repetition units RU adjacent to each other (namely, the boundary where the repetition unit RU is switched from one to another repetition unit RU) as in a boundary portion between the repetition units RU having the ideal phase distribution shown in
Next, a configuration for realizing a function (hereinafter, referred to as a “non-reflection function”) of suppressing the reflection of a terahertz wave at the interface (namely, a surface along which the outer end portions 3a are aligned) between the uneven structure 3 or 3A and air will be described. Such a configuration is realized by using the point that not only the diameter d but also the height h of the unevenness forming portion (the pillar 31 or the hole 32) can be changed for each of the regions A1 to A9 in the uneven structure 3 or 3A. In the following description, the case of using the uneven structure 3A shown in
In the following description, the meaning of each parameter is as follows.
-
- λ: wavelength of a terahertz wave to be operated
- p: period of the hole 32 (distance between the centers of the holes 32 adjacent to each other)
- r1: hole radius (radius of the hole 32) of the region A1
- ri: hole radius of a region Ai (i≥2)
- h1: height in the region A1 (height of the hole 32 included in the region A1)
- hi: height in the region Ai (height of the hole 32 included in the region Ai)
- nAir: refractive index of an air layer
- nsub: refractive index of a portion with which the material (high-resistance silicon) of the substrate 2 is filled (namely, a portion in which the uneven structure 3A (hole 32) is not formed in the substrate 2)
- neff1: effective refractive index of the region A1
- neffi: effective refractive index of the region Ai
When a hole radius r1 is determined to be a random value, the height h1 is set based on the following equation (5), so that the non-reflection function can be realized in the region A1.
Here, an effective refractive index neff1 of the region A1 is determined by the hole radius r1 of the region A1 based on the following equation (6).
Namely, the height h1 for realizing the non-reflection function in the region A1 is determined by the hole radius r1. A hole radius r, that generates a desired phase difference ϕi with respect to the region A1 and can realize the non-reflection function in any region Ai can be obtained as follows based on the premise of the above description.
First, the phase modulation amount generated in the region A1 is expressed by the following equation (7). In addition, the phase modulation amount generated in the region Ai is expressed by the following equation (8).
(neff1·h1)+nsub(hi−h1) (7)
(neff1·hi) (8)
The desired phase difference ϕi is expressed from the above equations (7) and (8) by the following equation (9).
The above equation (9) is modified to obtain the following equation (10).
Here, since neffi is expressed by the above equation (6), neffi can be expressed as a function “neff(ri)” of the hole radius ri. Furthermore, the microloading effect in the region Ai (here, a difference between the height in the region Ai and the height in the region A1 caused by the microloading effect) can be also expressed as a function “M.1(ri)” of the hole radius ri of the region Ai. Namely, the height in the region Ai can be expressed as in the following equation (11).
hi=h1+M.1(ri) (11)
As a result, the following equation (12) is obtained from the above equations (10) and (11).
Here, since h1 and nsub are constants, the left side of the above equation (12) can be expressed as a function “G(ri)” of which the value is determined by the hole radius ri. Namely, the above equation (12) is expressed as in the following equation (13).
Therefore, when the hole radius ri of the region Ai is set to satisfy the above equation (13), in the region Ai, the desired phase difference ϕi can be generated with respect to the region A1 and the non-reflection function can be realized. Namely, in the above example, first, a combination of the hole radius r1 and the height h1 in the region A1 is determined to satisfy the above equation (5). The hole radius r1 for obtaining the above combination is determined in consideration of the microloading effect. Specifically, the hole radius r1 can be determined based on information (information corresponding to the information shown in
Incidentally, here, the case of using the uneven structure 3A has been described; however, even when the uneven structure 3 is used, the non-reflection function can be realized in each of the regions A1 to A9 according to the same approach described above. Specifically, when the uneven structure 3 is used, an equation that is similar to the above equation (13) and has a function of the radius of the pillar 31 of the region Ai on the left side can be derived. Then, the radius of the pillar 31 which satisfies the equation is calculated for each region and the above-described steps (S3 to S6 of
[Effects]
In the terahertz wave lens 1 described above, the height h and the diameter d of the unevenness forming portion (the pillar 31 in the case of the uneven structure 3 and the hole 32 in the case of the uneven structure 3A) forming the uneven structure 3 or 3A differ for each of the regions A1 to A9. Accordingly, a phase difference that differs for each of the regions A1 to A9 can be generated for a terahertz wave transmitted through the substrate 2. In addition, since the substrate 2 on the surface of which the uneven structure 3 or 3A is formed is used to be able to further reduce the thickness of the lens than that of a spherical lens or the like, the size of the lens can be reduced. Furthermore, since the height positions of the outer end portions 3a of the uneven structure 3 or 3A in the thickness direction D are aligned, the occurrence of an aberration can be suppressed.
In addition, in the terahertz wave lens 1, since the distance (period p) between the centers of the unevenness forming portions (the pillars 31 or the holes 32) adjacent to each other is constant, the design of the arrangement of the unevenness forming portions is facilitated. Specifically, when the period p of the unevenness forming portions is constant, since the above-described periodic structures (in the present embodiment, square regions each including one unevenness forming portion in a central portion) having a constant area may be regularly (in the present embodiment, in a grid pattern) arranged on a plane, the layout of the unevenness forming portions can be easily designed. Meanwhile, when the period p of the unevenness forming portions is not constant (for example, when the period p differs according to the diameter d of the unevenness forming portion), the size of the above-described periodic structure differs for each of the regions A1 to A9. In this case, a gap (gap between the periodic structures having different sizes) occurs in the vicinity of the boundary where the region is switched from one to another region, and the effective refractive index (phase difference) in the portion of the gap may deviate from the design value. In addition, in a situation where the periodic structures having different sizes are mixed in the regions A1 to A9, it is difficult to find out an optimum arrangement of the periodic structures in which such a gap does not occur (or the gap is very small). Since the period p is constant, such a problem can be avoided.
In addition, when the unevenness forming portion is the pillar 31 (namely, when the terahertz wave lens 1 includes the uneven structure 3), the larger the diameter d of the pillar 31 is, the lower the height h of the pillar 31 is (refer to
In addition, when the unevenness forming portion is the hole 32 (namely, when the terahertz wave lens 1 includes the uneven structure 3A), the larger the diameter d of the hole 32 is, the higher the height h of the hole 32 is (refer to
In addition, the plurality of regions included in one repetition unit RU are formed of nine regions from the region A1 to the region A9 that are arranged along the predetermined direction (in the present embodiment, the radial direction of the substrate 2 having a disk shape). Then, the effective refractive index of the plurality of regions A1 to A9 is further decreased in a stepwise manner as the region is shifted from the region A1 toward the region A9. According to the configuration, since the plurality of regions are arranged such that the effective refractive index is further decreased in a stepwise manner as the region is shifted from the region A1 toward the region A9, the terahertz wave lens 1 can serve as a refractive index distribution type lens.
In addition, the height h of the unevenness forming portion (the pillar 31 or the hole 32) belonging to each of the regions A1 to A9 is further increased as the region is shifted from the region A1 toward the region A9. According to the configuration, the phase difference between the regions A1 to A9 can be more efficiently generated than when only the diameter d of the unevenness forming portion differs for each of the regions A1 to A9.
In addition, the plurality of regions A1 to A9 include first phase difference regions (in the present embodiment, the regions A3 to A9) where the phase difference between the regions adjacent to each other is set to the first phase difference, and second phase difference regions (in the present embodiment, the regions A1 and A2) where the phase difference between the regions adjacent to each other is set to the second phase difference smaller than the first phase difference. According to the configuration, the phase distribution design can be more flexibly performed than when the phase differences between the regions are equal (normal phase distribution design shown in
In addition, when the unevenness forming portion is the pillar 31 (namely, when the terahertz wave lens 1 includes the uneven structure 3), at least one region (in the present embodiment, the regions A1 and A2) where the diameter d of the pillar 31 in the uneven structure 3 is the threshold value Δd determined in advance or more may be the second phase difference region. According to the same approach, when the unevenness forming portion is the hole 32 (namely, the terahertz wave lens 1 includes the uneven structure 3A), at least one region where the diameter d of the hole 32 in the uneven structure 3A is a threshold value determined in advance or less may be the second phase difference region. According to the configuration, in a portion in which the microloading effect is relatively remarkable and it is difficult to accurately produce the unevenness forming portion (the pillar 31 or the hole 32) having the diameter d and the height h corresponding to the phase distribution designed in advance, the step size of the phase difference between the regions is made small, so that a deviation (production error) of the phase distribution from the design value can be compensated.
In addition, the height h and the diameter d of the unevenness forming portion (the pillar 31 or the hole 32) corresponding to each of the plurality of regions A1 to A9 are sized so as to be able to suppress the reflection of a terahertz wave at the interface between the uneven structure 3 or 3A and air. According to the configuration, since a reflection prevention layer is not required to be provided separately from the unevenness forming portion, the reflection of a terahertz wave at the interface between the uneven structure 3 or 3A and air can be suppressed while an increase in size of the terahertz wave lens 1 is prevented.
In addition, as described above, a method for producing the terahertz wave lens 1 according to the present embodiment includes a first step of determining a pattern of the uneven structure 3 or 3A (design that takes into consideration the microloading effect described using
In addition, in the first step, the pattern of the uneven structure 3 or 3A is determined such that the amount of etching per unit area of each of the plurality of regions A1 to A9 is further increased as the region is shifted from the region A1 toward the region A9. Namely, when the uneven structure 3 is used, the pattern of the uneven structure 3 is determined such that the diameter d of the pillar 31 is further decreased as the region is shifted from the region A1 toward the region A9 (refer to
In addition, the first step includes a step of acquiring information (refer to
In addition, in the first step, the diameter d of the unevenness forming portion (the pillar 31 or the hole 32) arranged in each of the regions A1 to A9 is determined such that the plurality of regions A1 to A9 include first phase difference regions (in the present embodiment, regions where the phase difference is set with a step of π/4) and second phase difference regions (regions where a phase difference smaller than π/4 is set). According to the configuration, the phase distribution design can be more flexibly performed than when the phase differences between the regions A1 to A9 are equal.
In addition, when the uneven structure 3 is used, in the first step, the diameter d of the pillar 31 arranged in each of the regions A1 to A9 may be determined such that at least one region (in the present embodiment, the regions A1 and A2) where the diameter d of the pillar 31 in the uneven structure 3 is the threshold value Δd determined in advance or more is the second phase difference region. In addition, when the uneven structure 3A is used, in the first step, the diameter d of the hole 32 arranged in each of the regions A1 to A9 may be determined such that at least one region where the diameter d of the hole 32 in the uneven structure 3A is the threshold value determined in advance or less is the second phase difference region. In addition, in the first step, the diameter d of the unevenness forming portion (the pillar 31 or the hole 32) arranged in each of the regions A1 to A9 may be determined such that at least the region A1 forms the second phase difference region. According to the configuration, in a portion in which the microloading effect is relatively remarkable and it is difficult to accurately produce the unevenness forming portion having the diameter d and the height h corresponding to the phase distribution designed in advance, the step size of the phase difference between the regions A1 to A9 is made small, so that a deviation (production error) of the phase distribution from the design value can be compensated.
In addition, in the first step, the diameter d of the unevenness forming portion (the pillar 31 or the hole 32) arranged in each of the regions A1 to A9 is determined such that at least one of the plurality of repetition units RU has a phase distribution having a width larger than 2π. According to the configuration, it is possible to obtain the terahertz wave lens 1 which reduces a possibility that the width of the actual phase distribution is smaller than 2π in the repetition unit RU formed to have a phase distribution having a width larger than 2π.
In addition, in the first step, the diameter d of the unevenness forming portion arranged in each of the regions A1 to A9 is determined such that the height h and the diameter d of the unevenness forming portion (the pillar 31 or the hole 32) corresponding to each of the plurality of regions A1 to A9 are sized so as to be able to suppress the reflection of a terahertz wave at the interface between the uneven structure 3 or 3A and air. According to the configuration, the terahertz wave lens 1 in which the above-described non-reflection function is exhibited in each of the regions A1 to A9 can be obtained.
Modification ExamplesThe exemplary embodiment of the present disclosure has been described above; however, the present disclosure is not limited to the embodiment. For example, the material and the shape of each configuration are not limited to the above-described example.
In addition, in the uneven structure 3, the pillar 31 may not have a columnar shape. For example, the uneven structure 3 may include pillars having a prismatic shape (for example, a quadrangular prism shape). In this case, instead of the diameter d, the length of one side of the pillar may be used as the width of the pillar. Similarly, in the uneven structure 3A, the hole 32 may not have a columnar shape. For example, the uneven structure 3A may include holes having a prismatic shape (for example, a quadrangular prism shape). In this case, instead of the diameter d, the length of one side of the hole may be used as the width of the hole.
In addition, the periodic structures that have the same area and are formed of a plurality of the unevenness forming portions (the pillars 31 or the holes 32) may not necessarily be square regions. For example, the plurality of unevenness forming portions may be arranged in a triangular grid pattern. In this case, the periodic structures having the same area may be regular hexagonal regions.
In addition, the distance (period p) between the centers of the unevenness forming portions adjacent to each other may not necessarily be constant. However, since the distance between the centers of the unevenness forming portions is constant, as described above, there is an advantage that the design of the arrangement of the unevenness forming portions is facilitated.
In addition, the uneven structure 3 may include a pillar 31A illustrated in
In addition, the uneven structure 3A may include a hole 32A illustrated in
In addition, in the embodiment, the terahertz wave lens 1 in which the plurality of repetition units RU are concentrically with respect to the center (center P) of the lens is provided as an example; however, the form of the terahertz wave lens according to the present disclosure is not limited to the above form. For example, the terahertz wave lens according to the present disclosure may exhibit a lens function only in one axial direction like a cylindrical lens. For example, the repetition units RU and the plurality of regions A1 to A9 included in the repetition unit RU may be formed in a rectangular shape and may be arranged along one axial direction.
In addition, in the embodiment, the terahertz wave lens serving as a convex lens is provided as one example of a terahertz wave optical element; however, when the distribution of the effective refractive indexes (namely, the shape and the arrangement of the plurality of unevenness forming portions) in the uneven structure is adjusted, the terahertz wave lens including the substrate and the uneven structure described above may serve as a concave lens. In addition, the terahertz wave optical element including the substrate and the uneven structure described above is not limited to the terahertz wave lens. For example, the terahertz wave optical element according to the present disclosure may be an optical element other than lenses such as a polarizing plate, a wave plate, and a diffraction grating.
REFERENCE SIGNS LIST
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- 1: terahertz wave lens (terahertz wave optical element), 2: substrate, 3, 3A: uneven structure, 3a: outer end portion, 31, 31A: pillar (unevenness forming portion and protruding portion), 32, 32A: hole (unevenness forming portion and recessed portion), A1 to A9: region, D: thickness direction, RU: repetition unit.
Claims
1. A terahertz wave optical element comprising:
- a substrate having a surface provided with an uneven structure that changes a phase of a terahertz wave,
- wherein the uneven structure includes a plurality of unevenness forming portions formed of protruding portions extending from the surface that are periodically arranged,
- the uneven structure includes a plurality of regions where the plurality of unevenness forming portions are arranged,
- a height of the unevenness forming portion in a thickness direction of the substrate and a width of the unevenness forming portion in a direction orthogonal to the thickness direction differ for each of the regions,
- outer end portions of the uneven structure in the thickness direction are located on the same plane,
- the plurality of regions are formed of N, N is an integer of 2 or more, regions including a first region to an Nth region that are arranged along a predetermined direction, and
- an effective refractive index of each of the plurality of regions is further decreased in a stepwise manner as the region is shifted from the first region toward the Nth region.
2. The terahertz wave optical element according to claim 1,
- wherein a distance between centers of the unevenness forming portions adjacent to each other is constant.
3. The terahertz wave optical element according to claim 1,
- wherein the larger the width of the unevenness forming portion is, the higher the height of the unevenness forming portion is.
4. The terahertz wave optical element according to claim 1,
- wherein the height of the unevenness forming portion belonging to each of the regions is further increased as the region is shifted from the first region toward the Nth region.
5. The terahertz wave optical element according to claim 1,
- wherein the plurality of regions include a first phase difference region where a phase difference between the regions adjacent to each other is set to a first phase difference, and a second phase difference region where a phase difference between the regions adjacent to each other is set to a second phase difference smaller than the first phase difference.
6. The terahertz wave optical element according to claim 5,
- wherein at least one of the regions, in which the width of the unevenness forming portion in the uneven structure is a threshold value determined in advance or more, is the second phase difference region.
7. The terahertz wave optical element according to claim 5,
- wherein at least the first region forms the second phase difference region.
8. The terahertz wave optical element according to claim 1,
- wherein the unevenness forming portion includes a plurality of repetition units each including one set of the plurality of regions,
- the plurality of repetition units are arranged along the predetermined direction, and
- at least one of the plurality of repetition units is formed to have a phase distribution having a width larger than 2π.
9. The terahertz wave optical element according to claim 1,
- wherein the height and the width of the unevenness forming portion corresponding to each of the plurality of regions are sized so as to suppress reflection of the terahertz wave at an interface between the uneven structure and air.
10. A method for producing a terahertz wave optical element, the method comprising:
- a first step of determining a pattern of an uneven structure that changes a phase of a terahertz wave;
- a second step of forming an etching mask, which corresponds to the pattern, on a surface of a substrate that is flat;
- a third step of performing anisotropic etching on the substrate in a state where the etching mask is formed on the surface of the substrate, to form the uneven structure in the surface of the substrate, the uneven structure including a plurality of unevenness forming portions formed of protruding portions extending from the surface that are periodically arranged; and
- a fourth step of removing the etching mask from the surface of the substrate,
- wherein the uneven structure includes a plurality of regions where the plurality of unevenness forming portions are arranged,
- a height of the unevenness forming portion in a thickness direction of the substrate and a width of the unevenness forming portion in a direction orthogonal to the thickness direction differ for each of the regions,
- wherein in the first step, the pattern of the uneven structure is determined such that the plurality of regions are formed of N, N is an integer of 2 or more, regions including a first region to an Nth region that are arranged along a predetermined direction, and an amount of etching per unit area of each of the plurality of regions is further increased in a stepwise manner as the region is shifted from the first region toward the Nth region.
11. The method for producing a terahertz wave optical element according to claim 10, wherein in the first step, the pattern of the uneven structure is determined such that a distance between centers of the unevenness forming portions adjacent to each other is constant.
12. The method for producing a terahertz wave optical element according to claim 11,
- wherein the first step includes a step of acquiring information indicating a relationship between the width of the unevenness forming portion and an etching depth, and a step of determining the width of the unevenness forming portion, which is arranged in each of the regions, based on the information indicating the relationship and a design value of a phase distribution determined in advance.
13. The method for producing a terahertz wave optical element according to claim 10,
- wherein in the first step, the width of the unevenness forming portion arranged in each of the regions is determined such that the plurality of regions include a first phase difference region and a second phase difference region,
- the first phase difference region is a region where a phase difference between the regions adjacent to each other is set to a first phase difference, and
- the second phase difference region is a region where a phase difference between the regions adjacent to each other is set to a second phase difference smaller than the first phase difference.
14. The method for producing a terahertz wave optical element according to claim 13,
- wherein in the first step, the width of the unevenness forming portion arranged in each of the regions is determined such that at least one of the regions, in which the width of the unevenness forming portion in the uneven structure is a threshold value determined in advance or more, is the second phase difference region.
15. The method for producing a terahertz wave optical element according to claim 13,
- wherein in the first step, the width of the unevenness forming portion arranged in each of the regions is determined such that at least the first region forms the second phase difference region.
16. The method for producing a terahertz wave optical element according to claim 10,
- wherein in the first step, the width of the unevenness forming portion arranged in each of the regions is determined such that the unevenness forming portion includes a plurality of repetition units each including one set of the plurality of regions, the plurality of repetition units are arranged along the predetermined direction, and at least one of the plurality of repetition units has a phase distribution having a width larger than 2π.
17. The method for producing a terahertz wave optical element according to claim 10,
- wherein in the first step, the width of the unevenness forming portion arranged in each of the regions is determined such that the height and the width of the unevenness forming portion corresponding to each of the plurality of regions are sized so as to suppress reflection of the terahertz wave at an interface between the uneven structure and air.
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Type: Grant
Filed: Jun 14, 2023
Date of Patent: Nov 5, 2024
Patent Publication Number: 20230324591
Assignee: HAMAMATSU PHOTONICS K.K. (Hamamatsu)
Inventors: Shohei Hayashi (Hamamatsu), Tetsushi Shimomura (Hamamatsu), Hiroyasu Fujiwara (Hamamatsu)
Primary Examiner: Christopher Stanford
Assistant Examiner: Journey F Sumlar
Application Number: 18/209,718